Multiplicative white-noise-induced phase transitions: the role of the stochastic interpretation

2004 ◽  
Author(s):  
Jose M. Sancho ◽  
Oliver Carrillo ◽  
Marta Ibanes ◽  
Jaume Casademunt ◽  
Jordi Garcia-Ojalvo
Keyword(s):  
Phase Transitions ◽  
White Noise ◽  
Multiplicative White Noise

Random exponential attractor for second-order nonautonomous stochastic lattice systems with multiplicative white noise

2019 ◽  
Vol 19 (06) ◽  
pp. 1950044
Author(s):  
Haijuan Su ◽  
Shengfan Zhou ◽  
Luyao Wu
Keyword(s):  
White Noise ◽  
Weighted Space ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lattice System ◽  
Exponential Attractor ◽  
Lattice Systems ◽  
Random System ◽  
Multiplicative White Noise ◽  
Infinite Sequences

We studied the existence of a random exponential attractor in the weighted space of infinite sequences for second-order nonautonomous stochastic lattice system with linear multiplicative white noise. Firstly, we present some sufficient conditions for the existence of a random exponential attractor for a continuous cocycle defined on a weighted space of infinite sequences. Secondly, we transferred the second-order stochastic lattice system with multiplicative white noise into a random lattice system without noise through the Ornstein–Uhlenbeck process, whose solutions generate a continuous cocycle on a weighted space of infinite sequences. Thirdly, we estimated the bound and tail of solutions for the random system. Fourthly, we verified the Lipschitz continuity of the continuous cocycle and decomposed the difference between two solutions into a sum of two parts, and carefully estimated the bound of the norm of each part and the expectations of some random variables. Finally, we obtained the existence of a random exponential attractor for the considered system.

scholarly journals The role of Ni-Mn hybridization on the martensitic phase transitions in Mn-rich Heusler alloys

2012 ◽  
Vol 100 (17) ◽  
pp. 172403 ◽  
Author(s):  
Mahmud Khan ◽  
J. Jung ◽  
S. S. Stoyko ◽  
Arthur Mar ◽  
Abdiel Quetz ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Heusler Alloys ◽  
Martensitic Phase ◽  
Martensitic Phase Transitions

Response to ‘‘Role of nonperturbative field configurations in phase transitions.’’

1986 ◽  
Vol 34 (2) ◽  
pp. 662-663
Author(s):  
Hideaki Aoyama ◽  
Helen R. Quinn
Keyword(s):  
Phase Transitions

scholarly journals Role of Twinning in Perovskite-Lithium Niobate Phase Transitions.

1998 ◽  
Vol 7 ◽  
pp. 40-43 ◽  
Author(s):  
Charles T. Prewitt ◽  
Taegyung Ko ◽  
Guoyin Shen ◽  
John D. Fitz Gerald
Keyword(s):  
Phase Transitions ◽  
Lithium Niobate
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